Calculus Workbook for Dummies, 3rd Edition

Description

The easy way to conquer calculus Calculus is hard--no doubt about it--and students often need help understanding or retaining the key concepts covered in class. Calculus Workbook For Dummies serves up the concept review and practice problems with an easy-to-follow, practical approach. Plus, you'll get free access to a quiz for every chapter online. With a wide variety of problems on everything covered in calculus class, you'll find multiple examples of limits, vectors, continuity, differentiation, integration, curve-sketching, conic sections, natural logarithms, and infinite series. Plus, you'll get hundreds of practice opportunities with detailed solutions that will help you master the math that is critical for scoring your highest in calculus. Review key concepts Take hundreds of practice problems Get access to free chapter quizzes online Use as a classroom supplement or with a tutor Get ready to quickly and easily increase your confidence and improve your skills in calculus. Title Page......Page 3 Copyright Page......Page 4 Table of Contents......Page 7 About This Book......Page 11 Icons Used in This Book......Page 12 Where to Go from Here......Page 13 Part 1 Pre-Calculus Review......Page 15 Fraction Frustration......Page 17 Misc. Algebra: You Know, Like Miss South Carolina......Page 19 Geometry: When Am I Ever Going to Need It?......Page 21 Solutions for This Easy, Elementary Stuff......Page 26 Figuring Out Your Functions......Page 35 Trigonometric Calisthenics......Page 39 Solutions to Functions and Trigonometry......Page 43 Part 2 Limits and Continuity......Page 51 Chapter 3 A Graph Is Worth a Thousand Words: Limits and Continuity......Page 53 Digesting the Definitions: Limit and Continuity......Page 54 Taking a Closer Look: Limit and Continuity Graphs......Page 56 Solutions for Limits and Continuity......Page 60 Chapter 4 Nitty-Gritty Limit Problems......Page 63 Solving Limits with Algebra......Page 64 Pulling Out Your Calculator: Useful “Cheating”......Page 69 Making Yourself a Limit Sandwich......Page 71 Into the Great Beyond: Limits at Infinity......Page 73 Solutions for Problems with Limits......Page 77 Part 3 Differentiation......Page 87 The Derivative: A Fancy Calculus Word for Slope and Rate......Page 89 The Handy-Dandy Difference Quotient......Page 91 Solutions for Differentiation Basics......Page 94 Rules for Beginners......Page 99 Giving It Up for the Product and Quotient Rules......Page 102 Linking Up with the Chain Rule......Page 104 What to Do with Y’s: Implicit Differentiation......Page 108 Getting High on Calculus: Higher Order Derivatives......Page 111 Solutions for Differentiation Problems......Page 113 The First Derivative Test and Local Extrema......Page 127 The Second Derivative Test and Local Extrema......Page 130 Finding Mount Everest: Absolute Extrema......Page 132 Smiles and Frowns: Concavity and Inflection Points......Page 136 The Mean Value Theorem: Go Ahead, Make My Day......Page 139 Solutions for Derivatives and Shapes of Curves......Page 141 Optimization Problems: From Soup to Nuts......Page 157 Problematic Relationships: Related Rates......Page 160 A Day at the Races: Position, Velocity, and Acceleration......Page 163 Solutions to Differentiation Problem Solving......Page 167 Make Sure You Know Your Lines: Tangents and Normals......Page 183 Looking Smart with Linear Approximation......Page 187 Calculus in the Real World: Business and Economics......Page 189 Solutions to Differentiation Problem Solving......Page 193 Part 4 Integration and Infinite Series......Page 201 Adding Up the Area of Rectangles: Kid Stuff......Page 203 Sigma Notation and Riemann Sums: Geek Stuff......Page 206 Close Isn’t Good Enough: The Definite Integral and Exact Area......Page 210 Finding Area with the Trapezoid Rule and Simpson’s Rule......Page 212 Solutions to Getting into Integration......Page 215 The Absolutely Atrocious and Annoying Area Function......Page 223 Sound the Trumpets: The Fundamental Theorem of Calculus......Page 226 Finding Antiderivatives: The Guess- and-Check Method......Page 229 The Substitution Method: Pulling the Switcheroo......Page 231 Solutions to Reverse Differentiation Problems......Page 235 Integration by Parts: Here’s How u du It......Page 239 Transfiguring Trigonometric Integrals......Page 243 Trigonometric Substitution: It’s Your Lucky Day!......Page 245 Partaking of Partial Fractions......Page 247 Solutions for Integration Rules......Page 251 Finding a Function’s Average Value......Page 265 Finding the Area between Curves......Page 266 Volumes of Weird Solids: No, You’re Never Going to Need This......Page 268 Arc Length and Surfaces of Revolution......Page 275 Solutions to Integration Application Problems......Page 278 Chapter 14 Infinite (Sort of) Integrals......Page 287 Getting Your Hopes Up with L’Hôpital’s Rule......Page 288 Disciplining Those Improper Integrals......Page 290 Solutions to Infinite (Sort of) Integrals......Page 293 The Nifty nth Term Test......Page 297 Testing Three Basic Series......Page 299 Apples and Oranges . . . and Guavas: Three Comparison Tests......Page 301 Ratiocinating the Two “R” Tests......Page 305 He Loves Me, He Loves Me Not: Alternating Series......Page 307 Solutions to Infinite Series......Page 309 Part 5 The Part of Tens......Page 319 The 33333 Mnemonic......Page 321 Fourth 3 over the “i”: 3 cases where continuity fails to exist......Page 322 First 3: The three tests with names......Page 323 The 2 in the middle: The two R tests......Page 324 The First Derivative Is a Rate......Page 325 Inflection Points and Sign Changes in the Second Derivative......Page 326 “PSST,” Here’s a Good Way to Remember the Derivatives of Trig Functions......Page 327 Index......Page 329 EULA......Page 339